A buffer solution is typically an aqueous solution comprising a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid, and has the property that the pH of the solution changes very little when a small amount of strong acid or base is added to it. Buffer solutions are therefore used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications, including e.g. chromatography, filtration, etc. In general, a buffer solution may be made up of more than one weak acid and its conjugate base. For instance, a wider buffer region may be created by mixing two buffering agents with overlapping individual buffer regions.
A buffer solution having a desired pH, and optionally also ionic strength, may be prepared by calculating the necessary amounts of the ingredients of the buffer and mixing them. While it is often necessary to solve several different equations for calculating the pH of a relatively simple mixture of a weak acid (or base) and a strong base (or acid) depending on their relative concentrations, there is commercial software available for performing such calculations. For many applications, it would be desirable to also be able to predict the expected error in the pH value of the buffer to be prepared with respect to variation in the amounts of the buffer components and to the presence of contaminants. Usually different types of “rules of thumb” are applied for instance +/−1.0 or 0.5 pH units from the thermodynamic pKa value. However these rules of thumb are only gross approximations and do not take into consideration the buffer concentration whereas it is well known that the buffer concentration is very important factor determining the accuracy of a buffer. A better alternative is to use, the calculated buffer capacity defined as the calculated number of moles of strong acid or base that give rise to a change in one pH unit per unit volume of solution as guidance to determine a valid pH interval. As opposed to the named “rules of thumb” the buffer capacity takes into consideration the buffer concentration. Furthermore, calculations of buffer capacity can be made even taking into consideration the shifts in the pKa values due to ionic activity (US 2011/0039712). However it is usually not clear which value of the buffer capacity to use as a threshold to decide if the buffer is accurate enough. Another disadvantage of using only the buffer capacity is that it does not take into consideration the incoming error of the amounts of buffer components, e.g. due to metering pump inaccuracies. Yet another disadvantage of the buffer capacity is that its calculation generally does not take into consideration the solubility limits of the buffer. On the contrary buffer capacity calculations usually suggest only a lower limit of the buffer concentration and predict smaller errors at higher buffer concentrations. In practice however, increasing the buffer concentration without knowledge of the buffer solubility limits may lead to precipitation when the solubility limit of the least soluble buffer component is exceeded. In general, due to the complex nature of buffers solutions, being combinations of strong electrolytes like salts and strong acids or bases that dissociate completely and weak electrolytes like buffer substances that ionize partially, reliable calculations of pH intervals of a buffer at which to expect a pH error within a beforehand decided value has so far not been possible and to our knowledge previously not been described before.